We analyze inequality and mobility across generations in a dynastic economy. The schooling of each generation is observable but ability is hidden, stochastic and persistent across generations. We calibrate the economy to U.S. data and compare the implied inequality and mobility patterns in the steady state to the inequality and mobility in the transition from this steady state to the social optimum. We find that, on this transition path, mobility in consumption decreases as more insurance against ability shocks is provided. Because of this additional insurance, dynastic welfare depends more on the observable schooling and bequests.